Theory:

To subtract two trinomials, you must:
 
1) remove the brackets and change the signs of the trinomials that are preceded by the sign "\(- \)" to the opposite;
2) combine the like terms of the trinomials.
Example:
Let us calculate the difference of trinomials (7x2+3x2) and 2x2+2x+3
  
1) Write down the difference of the trinomials and remove the brackets, taking the signs before the brackets into account:
 
(7x2+3x2)(2x2+2x+3)=7x2+3x2+2x22x3
 
2) Find the like terms:
 
7x2¯+3x¯¯2+2x2¯2x¯¯3
 
3) Combine the like terms:
 
7x2¯+3x¯¯2+2x2¯2x¯¯3=(7+2)x2+(32)x23=9x2+1x5
 
4) If the coefficient of a term is \(1\), then usually we do not write it:
 
9x2+1x5=9x2+x5
Important!
Remember: the sum or the difference of trinomials is always a trinomial.
To find the opposite of a trinomial, change the signs of the coefficients of all terms to the opposite.
Example:
The opposite of 
2m2n+3mn4 is
2m2n3mn+4
 
The opposite of 
7a22,5a8 is
7a2+2,5a+8
 
The opposite of 
xn0,05 is
xn+0,05
Two trinomials are called opposite if their sum is \(0\).
Example:
Trinomials 4a2b+3ab+2 and 4a2b3ab2 are opposite, because their sum is zero:
 
4a2b+3ab+2+4a2b3ab+2=
 
4a2b+3ab+2+4a2b3ab2==3ab+23ab2=22=0